An Energy Balance Criterion for Nanoindentation-Induced Single and Multiple Dislocation Events

[+] Author and Article Information
William W. Gerberich

Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue, SE, Minneapolis, MN 55455wgerb@umn.edu

W. M. Mook, M. D. Chambers, M. J. Cordill, C. R. Perrey, C. B. Carter

Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue, SE, Minneapolis, MN 55455

R. E. Miller

Mechanical and Aerospace Engineering, Carleton University, Ottawa, ON K1S 5B6, Canada

W. A. Curtin

Division of Engineering, Brown University, Providence, RI 02912

R. Mukherjee, S. L. Girshick

Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455

J. Appl. Mech 73(2), 327-334 (Aug 01, 2005) (8 pages) doi:10.1115/1.2125988 History: Received August 27, 2004; Revised August 01, 2005

Small volume deformation can produce two types of plastic instability events. The first involves dislocation nucleation as a dislocation by dislocation event and occurs in nanoparticles or bulk single crystals deformed by atomic force microscopy or small nanoindenter forces. For the second instability event, this involves larger scale nanocontacts into single crystals or their films wherein multiple dislocations cooperate to form a large displacement excursion or load drop. With dislocation work, surface work, and stored elastic energy, one can account for the energy expended in both single and multiple dislocation events. This leads to an energy balance criterion which can model both the displacement excursion and load drop in either constant load or fixed displacement experiments. Nanoindentation of Fe-3% Si (100) crystals with various oxide film thicknesses supports the proposed approach.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Examples of “staircase yielding” in both (a) experimental (4) and (b) simulation (5) results

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Figure 2

(a) Representative transmission electron micrograph of a silicon nanoparticle. (b) Load-displacement results of the repeated compression of a 39nm diameter silicon nanosphere. The inset shows the initial compression of the nanosphere with distinct displacement excursions.

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Figure 3

Idealized compression of a nanosphere

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Figure 4

Stress-depth curves for the four dislocation loops formed when compressing a 38.6nm silicon nanosphere. The initial work is governed by the crossing point with a Peierls stress of 4GPa which also defines the arrest position.

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Figure 5

(a) From Van Vliet (20), the simulated force-displacement curve for an indentation into aluminum crystal and (b) the corresponding stress-depth curves using the present model in conjunction with their data for six loops. The second load-drop at B was not considered to correspond to a dislocation loop formation.

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Figure 6

Comparison of instability magnitudes from Eq. 18 for displacement control tests with one film thickness and for load control tests with four film thicknesses



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